10 problems

Fix $lambda>0$ and $phi>0$, and let $\hat{x}_{\mathrm{upper}}$ be the supremum of the inflection points defined in Theorem 2 for the absolute-error Gamma family. Absolute-tail boun…

Let $\bar{x}_{\mathrm{upper}}$ and $\bar{x}_{\mathrm{lower}}$ be the points defined in Theorem 1 for the relative-error Gamma family, with effective shape parameter $\mu$. Extremal…

Nonexistence conjecture. There is no estimator $\mathscr T$ satisfying this equation when both $\kappa_1$ and $\kappa_2$ are unknown.

Let $Xa= sum{i=1}^n aiXi$ and $Xb=sum{i=1}^n biXi$, where $X1,ldots,Xn$ are i.i.d. Gamma random variables with parameter $alpha$, and let $aprec b$ denote majorization of the coeff…

Behme–Bondesson conjecture. The same conclusion remains true for all $k>0$:

Diaconis–Perlman unique crossing conjecture. If $\eta\prec\theta$, but $\theta$ is not a permutation of $\eta$, then $F_\eta(x)-F_\theta(x)$ changes signs exactly once, from $-$ to…

Let $\gamma_t$ and $\gamma_s$ be independent gamma random variables with parameters $t,s>0$. The gamma-product conjecture. For all $s,t>0$, the independent product…

Let $n\geqslant2$ and $\textbf{Y}=(Y_1,Y_2,\ldots,Y_n)$ be a vector of i.i.d. random variables. Let $G_a$ denote a gamma random variable with parameter $a$, and let $B_{a,b}$ denot…

All-order Laguerre conjecture. One might conjecture that

Normalized Laguerre order-2 conjecture. For any random variable $X$ and any $k\in\mathbb{N}$,